3.1: MIXING JUICE Big Idea:Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Essential question: What methods can we use to compare?
3.1 A. Which recipe will make juice that is the most “orangey”? Explain your answer. Mix A is the most ‘orangey’, because Mix A = 40% concentrate or 2 to 5. B. Which recipe will make juice that is the least “orangey”? Explain your answer. Mix B is the last ‘orangey’, because Mix B = 20% concentrate or ¼ (0.25 cups of concentrate per one cup of water). C. Assume that each camper will get ½ cup of juice. For each recipe, how much concentrate and how much water are needed to make juice for 24 campers? Explain your answer. Answer: One half of 240 = 120 (120 cups of juice of 240 of the campers.) Mix A = 48 cups (0.4 x 120) of concentrate and 72 (0.6 x 120) cups of water. Mix B = 24 cups (0.2 x 120) of concentrate and 96 cups (0.8 x 120) of water. Mix C = 40 cups (0.33 x 120) of concentrate and 80 cups (0.67 x 120) of water. Mix D =45 cups (0.375 x 120) of concentrate and 75 cups (0.625 x 120) of water. Follow Up 1. How did you use ratios in solving Problem 3.1? I used ratios to see which recipe for juice was more or less and then I used those ratios to help me find percentages of the amounts.
2. For each recipe, how much concentrate and how much water is needed to make 1 cup of juice Mix A = 0.4 of orange concentrate and 0.6 water.
Mix B = 0.2 of orange concentrate and 0.8 water . Mix C = 0.33 of orange concentrate and 0.67 water.
Mix D = 0.375 of orange concentrate and 0.625 water.
Big Idea: Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Essential question: What methods can we use to compare?
3.1
A. Which recipe will make juice that is the most “orangey”? Explain your answer. Mix A is the most ‘orangey’, because Mix A = 40% concentrate or 2 to 5.
B. Which recipe will make juice that is the least “orangey”? Explain your answer. Mix B is the last ‘orangey’, because Mix B = 20% concentrate or ¼ (0.25 cups of concentrate per one cup of water).
C. Assume that each camper will get ½ cup of juice. For each recipe, how much concentrate and how much water are needed to make juice for 24 campers? Explain your answer. Answer: One half of 240 = 120 (120 cups of juice of 240 of the campers.) Mix A = 48 cups (0.4 x 120) of concentrate and 72 (0.6 x 120) cups of water. Mix B = 24 cups (0.2 x 120) of concentrate and 96 cups (0.8 x 120) of water. Mix C = 40 cups (0.33 x 120) of concentrate and 80 cups (0.67 x 120) of water. Mix D =45 cups (0.375 x 120) of concentrate and 75 cups (0.625 x 120) of water.
Follow Up
1. How did you use ratios in solving Problem 3.1?
I used ratios to see which recipe for juice was more or less and then I used those ratios to help me find percentages of the amounts.
2. For each recipe, how much concentrate and how much water is needed to make 1 cup of juice
Mix A = 0.4 of orange concentrate and 0.6 water.
Mix B = 0.2 of orange concentrate and 0.8 water
.
Mix C = 0.33 of orange concentrate and 0.67 water.
Mix D = 0.375 of orange concentrate and 0.625 water.